"The appeal was filed a couple of days ago and the Supreme Court is deciding whether to consider it," said Pavel Odintsov, the Supreme Court's press secretary.
Odintsov said the Russian Code of Civil Procedure provides that such a decision must be made within four months.
On Thursday, Bailiffs started to tear down country houses illegally built on the bank of the Istra reservoir outside Moscow.
The spokesman said the appeal would not affect the procedure of implementing the court's decision.
"The court of cassation has already made and enforced the decision, which the bailiffs are obliged to implement," he said.
If the court decides to consider the appeal, applicants could push for a stay of execution. "However, there are many ifs in the way, and these speculations are hypothetical," Odintsov said.